MachineSex/results/E6

E6 — Re-minting is irreversible; gate it on diversity

Claim tested: what happens if you "re-baseline" — declare the current model's output to be the new ground truth and throw away the original? If you do this while the model is already collapsed, is the damage permanent? And can a simple safeguard prevent it?

Setup (Layer 1, pure math). K = 500, n = 200, 400 generations, 100 repeats. Re-minting periodically freezes the current distribution as the new grounding reference and discards the original truth (it survives only as a yardstick for measuring drift). Four arms:

• healthy re-mint — generous grounding (m = 60), re-mint while still diverse;
• collapsed re-mint (ungated) — starved grounding (m = 1), re-mint anyway;
• collapsed + diversity gate — same starvation, but only re-mint if diversity H ≥ 0.75;
• collapsed, no re-mint — the baseline.

Symbols

• re-mint — adopt the current model's output as the new "reality" and discard the original truth (a founder event).
• diversity gate — refuse to re-mint while H is below a threshold (here 0.75).
• forward-KL to ORIGINAL truth — how far the lineage has drifted from the real original, even after it changed its own reference.

The two panels

1. Lock-in. Forward-KL to the original truth over generations; dotted verticals mark re-mint events. Red (collapsed, ungated) jumps up at each re-mint and never comes back — once the original tails are gone, re-baselining onto the impoverished distribution makes the loss permanent (they can no longer be grounded back). Green (healthy) and blue (gated) stay low; grey (baseline) is the reference.
2. What the gate reads. Diversity H over generations, same colour key, with the gate threshold (H = 0.75, dashed). The gated arm simply refuses to re-mint while below the line, so it never locks in a collapsed state; the ungated collapsed arm re-mints into the floor.

Takeaway

Re-minting a collapsed model crystallises the collapse — it is a one-way door. A trivial safeguard (only re-baseline when diversity is still high) preserves recoverability; re-minting a healthy model is harmless. Falsifier (not triggered): if the collapsed lineage had recovered its original tails after re-minting, the irreversibility claim would be overstated.